Janet M' Wang

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Extended Krylov Subspace Method for Reduced Order
Analysis of Linear Circuits with Multiple Sources

• Janet M. Wang
• Tuyen V. Nguyen

University of California at Berkeley,
CA94706 IBM Austin Research Laboratory ,
Austin, TX 78758
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Outline

• Introduction
• Power grid analysis
• Multiport reduced order modeling of the power
  grid
• Input dependent explicit moment matching
• Extended Krylov subspace method
• Incremetal orthogonalization algorithm
• mulpoint extension
• Practical considerations
• Scaling
• Error control
• Experimental results
• Conclusions

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Introduction
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Introduction
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Outline

• Introduction
• Power grid analysis
• Multiport reduced order modeling of the power
  grid
• Input dependent explicit moment matching
• Extended Krylov subspace method
• Incremetal orthogonalization algorithm
• mulpoint extension
• Practical considerations
• Scaling
• Error control
• Experimental results
• Conclusions

6
Power grid analysis

• Multiport reduced order modeling of the power
  grid
• Input dependent explicit moment matching

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Multiport reduced order modeling of the power
grid
Krylov subspace
The longer the u vector, the bigger the reduced
order matrices
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Input dependent explicit moment matching
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Input dependent explicit moment matching
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Input dependent explicit moment matching
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Input dependent explicit moment matching
12
Outline

• Introduction
• Power grid analysis
• Multiport reduced order modeling of the power
  grid
• Input dependent explicit moment matching
• Extended Krylov subspace method
• Incremetal orthogonalization algorithm
• mulpoint extension
• Practical considerations
• Scaling
• Error control
• Experimental results
• Conclusions

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Extended Krylov Subspace method
Input source moments
Congruence transform matrix
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Incremental Orthogonalization algorithm
At
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Incremental Orthogonalization algorithm
At
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Incremental Orthogonalization algorithm
At
For j1k-1
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Incremental Orthogonalization algorithm

• Theorem 1 The orthonormal vectors generated
  by the above algorithm span the same space as the
  original moment vectors

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Multipoint Extension
In order to capture higher frequency content of
the input waveforms